|1964 Lotus 34*|
160 piece jigsaw puzzle
Working on jigsaw puzzles is one of my favorite pass times these days. My standard procedure is pick out all of the edge pieces and work inward from there. The funny thing is that I often get a pair of tiles that connect even though I have only sorted through a few of the pieces, so now I'm wondering what are the odds? Say you have a 10 by 12 puzzle. You're going to have 120 pieces all told and 40 of those pieces will be edge pieces. If you have picked out n edge pieces, what are the odds that the next edge piece you pull will be a match for any of your existing pieces?
Starting with the edge and working inward works with most puzzles, but it didn't work for the one shown above. Puzzle pieces come in a variety of shapes, usually with curving edges that interlock with each other. Not this one, here the pieces are simple quadrilaterals and some pieces that were not edge pieces also had sides that were either perfectly vertical or horizontal, so you couldn't tell if they were edge pieces or not. The fact that half of the pieces were pure black didn't help either. So for this puzzle, I started from the center where there was something to see and worked outward.
When we are playing Rummikub, at the start you are usually holding at least one group of three tiles (either a run or three of a kind). The longer you play, the more tiles are on the board, and so there are more opportunities to play. How many tiles need to be on the board for you to be able to play all the tiles you are holding? Another way to put it, is how many tiles do you need to play them all? If you have three tiles, and they are all the same number, then three is all you need. But what are the odds of having three of a kind? Likewise, if you have 30 tiles, what are the odds that you could combine all of them into runs or three or four of a kind? I am not sure there is a mathematical formula for it. It might take a simulation, which is right up my alley.
* The Lotus 34 was a British racing car built by Team Lotus for the 1964 Indianapolis 500. . . . At Indianapolis, Jim Clark qualified on the pole, joined by five other similar cars. The Dunlop tyres failed during the race, leading to Clark crashing and the second 34 being parked. - Wikipedia